A linear model for smooth DEA BCC frontiers. (February 2020) - Brandão, Luana Carneiro
Highlights: This paper proposes a new objective function for Smooth Data Envelopment Analysis. The new objective function embraces the classic principle of minimum extrapolation. With the new objective function, smooth models become linear problems. As a linear problem, the new smooth model is simpler than previous smooth models. The new smooth model is based on a different topology, studied herein. Abstract: Smooth Data Envelopment Analysis was first proposed in 2002 to solve the classic problem of multiple optimal solutions for extreme-efficient DMUs. Since then, several studies proposed improvements to smooth models. However, they remained Quadratic Problems with the same objective function. The present work proposes a new model for smooth Data Envelopment Analysis, based on a new objective function. An important advantage of the new model is that it is a Linear Problem, unlike previous smooth models, and therefore simpler to calculate. Simplifications, such as this one, are particularly important, because smooth models usually require laborious calculations, even for small examples. In this work, we study topological properties and other characteristics of the linear model with variable returns to scale. Finally, we use examples from the literature to compare results between models with the traditional and the linear objective functions. Even though the latter required simpler calculations, the results for both models were found to be the same in all examples. Moreover, we performed certain sensitivity analyses, and found that, in general, the linear objective function presented more appropriate results.